Cut the vanilla bean lengthwise and scrape out the seeds.
Place both the seeds and the pod in a saucepan along with the sugar, salt, water, milk, lemon juice and zest. Add only as much juice and zest as how lemon-y you want it to taste. I use the juice of 1.5 lemons and zest of one.
Heat the mixture until the sugar dissolves and it just begins to boil, about 7 minutes.
Add the 3 teaspoons of vodka and chill the mixture in the freezer until it just starts to freeze.
Beat the cream to soft peaks. While beating, slowly drizzle in all of the milk syrup mixture.
Churn in an ice cream maker until done, 35 minutes. Freeze overnight in the canister with plastic wrap pressed directly on the surface of the sherbet.